Differential equations/Trig

http://www.examsolutions.net/a-level-maths-papers/Edexcel/Core-Maths/Core-Maths-C4/2007-June/paper.php#Q8

See q8d. Trying to solve for t, but I don't know whether to be in radians or degrees. Which and why?

Thanks
Krishna

Reply 1

Hasufel

16

differential equation = calculus = radians

(radians is the only measure of angle which "works" in calculus.)

Reply 2

krisshP

OP

14

Original post by Hasufel

differential equation = calculus = radians

Ok, so always use radians?

Thanks
Krishna

Reply 3

Hasufel

16

not too sure - think it goes back to the days when degrees where "invented" to go along with the idea that it took 360 days for the earth to "circle" the sun (which it doesn`t - 365.4 days to traverse an ellipse).

it isnt a "natural" unit of measurement like the radian which related to the circle in the formulas for area and arc length, but a made up one - that , i think is the reason why mathmos (and anone else) doesn`t use degrees in calc.

Reply 4

lebron_23

2

Calculus involving tringonometric functions should always scream radians to you.

The reason behind that dates back to when the degree was introduced and what it actually represents. The degree actually has no direct link to a circle but was chosen arbitrarily as a unit to measure angles. One can only imagine that 360 was chosen because it divides nicely by so many numbers.

Radians, on the other hand, is what circles are actually made up of.

EDIT: If you want to think of it mathematically, it's all to do with limits and other messy stuff.

\lim \limits_{x\to\infty} \dfrac{sinx}{x} = \lim \limits_{h\to\infty} \dfrac{sin(0+h)-sin0}{h}

At least, I think?

(edited 9 years ago)

Reply 5

krisshP

OP

14

Original post by lebron_23

Calculus involving tringonometric functions should always scream radians to you.

The reason behind that dates back to when the degree was introduced and what it actually represents. The degree actually has no direct link to a circle but was chosen arbitrarily as a unit to measure angles. One can only imagine that 360 was chosen because it divides nicely by so many numbers.

Radians, on the other hand, is what circles are actually made up of.

EDIT: If you want to think of it mathematically, it's all to do with limits and other messy stuff.